Estimation of the Location and Scale Parameters of Generalized Pareto Distribution Based on Progressively Type-II Censored Order Statistics

Based on progressively type-II right censored order statistics, we establish several recurrence relations for the single and product moments from the generalized Pareto distribution due to Pikands (1975). Further, recursive computational algorithm is provided which enable us to compute all the means...

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Bibliographic Details
Published in:Annals of data science Vol. 10; no. 2; pp. 349 - 383
Main Authors: Kumar, Devendra, Nassar, Mazen, Malik, Mansoor Rashid, Dey, Sanku
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2023
Springer Nature B.V
Subjects:
Algorithms
Artificial Intelligence
Business and Management
Data science
Economics
Failure
Finance
Insurance
Management
Maximum likelihood estimators
Maximum likelihood method
Monte Carlo simulation
Parameters
Probability distribution functions
Statistics
Statistics for Business
Progressively type-II right-censored order statistics
Single moments
Product moments
Generalized Pareto distribution
Recurrence relations
Best linear unbiased estimators
ISSN:2198-5804, 2198-5812
Online Access:Get full text
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Summary:Based on progressively type-II right censored order statistics, we establish several recurrence relations for the single and product moments from the generalized Pareto distribution due to Pikands (1975). Further, recursive computational algorithm is provided which enable us to compute all the means, variances and covariances for all sample sizes n , effective sample sizes m , and all progressive censoring schemes ( R 1 , … , R m ) . These relations generalize the results given by Aggarwala and Balakrishnan (Ann Inst Stat Math 48:757–771, 1996) and Joshi (Sankhyd Set B 39:362–371, 1978) for standard exponential distribution. Besides, these moments are then utilized to derive best linear unbiased estimators (BLUEs) of the scale and location parameters of the generalized Pareto distribution. Next, we obtain the maximum likelihood estimators of the unknown parameters of the model under progressively type-II right censored order statistics. Monte Carlo simulations are performed to compare the performances of the proposed method, and a numerical example is presented to illustrate the method developed here to obtain BLUEs.
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ISSN:2198-5804
2198-5812
DOI:10.1007/s40745-020-00266-0